{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Mixture Density Networks\n",
    "\n",
    "Mixture density networks (MDN) (Bishop, 1994) are a class\n",
    "of models obtained by combining a conventional neural network with a\n",
    "mixture density model.\n",
    "\n",
    "We demonstrate with an example in Edward. A webpage version is available at\n",
    "http://edwardlib.org/tutorials/mixture-density-network."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import absolute_import\n",
    "from __future__ import division\n",
    "from __future__ import print_function\n",
    "\n",
    "import edward as ed\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import seaborn as sns\n",
    "import tensorflow as tf\n",
    "\n",
    "from edward.models import Categorical, Mixture, Normal\n",
    "from scipy import stats\n",
    "from sklearn.model_selection import train_test_split"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def plot_normal_mix(pis, mus, sigmas, ax, label='', comp=True):\n",
    "  \"\"\"Plots the mixture of Normal models to axis=ax comp=True plots all\n",
    "  components of mixture model\n",
    "  \"\"\"\n",
    "  x = np.linspace(-10.5, 10.5, 250)\n",
    "  final = np.zeros_like(x)\n",
    "  for i, (weight_mix, mu_mix, sigma_mix) in enumerate(zip(pis, mus, sigmas)):\n",
    "    temp = stats.norm.pdf(x, mu_mix, sigma_mix) * weight_mix\n",
    "    final = final + temp\n",
    "    if comp:\n",
    "      ax.plot(x, temp, label='Normal ' + str(i))\n",
    "  ax.plot(x, final, label='Mixture of Normals ' + label)\n",
    "  ax.legend(fontsize=13)\n",
    "\n",
    "\n",
    "def sample_from_mixture(x, pred_weights, pred_means, pred_std, amount):\n",
    "  \"\"\"Draws samples from mixture model.\n",
    "\n",
    "  Returns 2 d array with input X and sample from prediction of mixture model.\n",
    "  \"\"\"\n",
    "  samples = np.zeros((amount, 2))\n",
    "  n_mix = len(pred_weights[0])\n",
    "  to_choose_from = np.arange(n_mix)\n",
    "  for j, (weights, means, std_devs) in enumerate(\n",
    "          zip(pred_weights, pred_means, pred_std)):\n",
    "    index = np.random.choice(to_choose_from, p=weights)\n",
    "    samples[j, 1] = np.random.normal(means[index], std_devs[index], size=1)\n",
    "    samples[j, 0] = x[j]\n",
    "    if j == amount - 1:\n",
    "      break\n",
    "  return samples"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Data\n",
    "\n",
    "We use the same toy data from\n",
    "[David Ha's blog post](http://blog.otoro.net/2015/11/24/mixture-density-networks-with-tensorflow/), where he explains MDNs. It is an inverse problem where\n",
    "for every input $x_n$ there are multiple outputs $y_n$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Size of features in training data: (3750, 1)\n",
      "Size of output in training data: (3750,)\n",
      "Size of features in test data: (1250, 1)\n",
      "Size of output in test data: (1250,)\n"
     ]
    },
    {
     "data": {
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B7asKnRnPXbR8Qm4fG7bdLyIicqepbcd/44dX8YOIQs7DWsufP3+Rnq4M+YyHH8YUywHT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\nSkRERESG8//bvUXcIhXA+gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x110da15d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def build_toy_dataset(N):\n",
    "  y_data = np.random.uniform(-10.5, 10.5, N)\n",
    "  r_data = np.random.normal(size=N)  # random noise\n",
    "  x_data = np.sin(0.75 * y_data) * 7.0 + y_data * 0.5 + r_data * 1.0\n",
    "  x_data = x_data.reshape((N, 1))\n",
    "  return train_test_split(x_data, y_data, random_state=42)\n",
    "\n",
    "\n",
    "ed.set_seed(42)\n",
    "\n",
    "N = 5000  # number of data points\n",
    "D = 1  # number of features\n",
    "K = 20  # number of mixture components\n",
    "\n",
    "X_train, X_test, y_train, y_test = build_toy_dataset(N)\n",
    "print(\"Size of features in training data: {}\".format(X_train.shape))\n",
    "print(\"Size of output in training data: {}\".format(y_train.shape))\n",
    "print(\"Size of features in test data: {}\".format(X_test.shape))\n",
    "print(\"Size of output in test data: {}\".format(y_test.shape))\n",
    "sns.regplot(X_train, y_train, fit_reg=False)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We define TensorFlow placeholders, which will be used to manually feed batches of data during inference. This is [one of many ways](http://edwardlib.org/api/data) to train models with data in Edward."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "X_ph = tf.placeholder(tf.float32, [None, D])\n",
    "y_ph = tf.placeholder(tf.float32, [None])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Model\n",
    "\n",
    "We use a mixture of 20 normal distributions parameterized by a\n",
    "feedforward network. That is, the membership probabilities and\n",
    "per-component mean and standard deviation are given by the output of a\n",
    "feedforward network.\n",
    "\n",
    "We use `tf.layers` to construct neural networks. We specify\n",
    "a three-layer network with 15 hidden units for each hidden layer."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def neural_network(X):\n",
    "  \"\"\"loc, scale, logits = NN(x; theta)\"\"\"\n",
    "  # 2 hidden layers with 15 hidden units\n",
    "  net = tf.layers.dense(X, 15, activation=tf.nn.relu)\n",
    "  net = tf.layers.dense(net, 15, activation=tf.nn.relu)\n",
    "  locs = tf.layers.dense(net, K, activation=None)\n",
    "  scales = tf.layers.dense(net, K, activation=tf.exp)\n",
    "  logits = tf.layers.dense(net, K, activation=None)\n",
    "  return locs, scales, logits\n",
    "\n",
    "\n",
    "locs, scales, logits = neural_network(X_ph)\n",
    "cat = Categorical(logits=logits)\n",
    "components = [Normal(loc=loc, scale=scale) for loc, scale\n",
    "              in zip(tf.unstack(tf.transpose(locs)),\n",
    "                     tf.unstack(tf.transpose(scales)))]\n",
    "y = Mixture(cat=cat, components=components, value=tf.zeros_like(y_ph))\n",
    "# Note: A bug exists in Mixture which prevents samples from it to have\n",
    "# a shape of [None]. For now fix it using the value argument, as\n",
    "# sampling is not necessary for MAP estimation anyways."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note that we use the `Mixture` random variable. It collapses\n",
    "out the membership assignments for each data point and makes the model\n",
    "differentiable with respect to all its parameters. It takes a\n",
    "`Categorical` random variable as input—denoting the probability for each\n",
    "cluster assignment—as well as `components`, which is a list of\n",
    "individual distributions to mix over.\n",
    "\n",
    "For more background on MDNs, take a look at\n",
    "[Christopher Bonnett's blog post](http://cbonnett.github.io/MDN.html) or at Bishop (1994)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Inference\n",
    "\n",
    "We use MAP estimation, passing in the model and data set.\n",
    "See this extended tutorial about\n",
    "[MAP estimation in Edward](http://edwardlib.org/tutorials/map)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# There are no latent variables to infer. Thus inference is concerned\n",
    "# with only training model parameters, which are baked into how we\n",
    "# specify the neural networks.\n",
    "inference = ed.MAP(data={y: y_ph})\n",
    "optimizer = tf.train.AdamOptimizer(5e-3)\n",
    "inference.initialize(optimizer=optimizer, var_list=tf.trainable_variables())"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here, we will manually control the inference and how data is passed\n",
    "into it at each step.\n",
    "Initialize the algorithm and the TensorFlow variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "sess = ed.get_session()\n",
    "tf.global_variables_initializer().run()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we train the MDN by calling `inference.update()`, passing\n",
    "in the data. The quantity `inference.loss` is the\n",
    "loss function (negative log-likelihood) at that step of inference. We\n",
    "also report the loss function on test data by calling\n",
    "`inference.loss` and where we feed test data to the TensorFlow\n",
    "placeholders instead of training data.\n",
    "We keep track of the losses under `train_loss` and `test_loss`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1000/1000 [100%] ██████████████████████████████ Elapsed: 21s | Loss: 4948.319\n"
     ]
    }
   ],
   "source": [
    "n_epoch = 1000\n",
    "train_loss = np.zeros(n_epoch)\n",
    "test_loss = np.zeros(n_epoch)\n",
    "for i in range(n_epoch):\n",
    "  info_dict = inference.update(feed_dict={X_ph: X_train, y_ph: y_train})\n",
    "  train_loss[i] = info_dict['loss']\n",
    "  test_loss[i] = sess.run(inference.loss,\n",
    "                          feed_dict={X_ph: X_test, y_ph: y_test})\n",
    "  inference.print_progress(info_dict)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note a common failure mode when training MDNs is that an individual\n",
    "mixture distribution collapses to a point. This forces the standard\n",
    "deviation of the normal to be close to 0 and produces NaN values.\n",
    "We can prevent this by thresholding the standard deviation if desired.\n",
    "\n",
    "After training for a number of iterations, we get out the predictions\n",
    "we are interested in from the model: the predicted mixture weights,\n",
    "cluster means, and cluster standard deviations.\n",
    "\n",
    "To do this, we fetch their values from session, feeding test data\n",
    "`X_test` to the placeholder `X_ph`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "pred_weights, pred_means, pred_std = sess.run(\n",
    "    [tf.nn.softmax(logits), locs, scales], feed_dict={X_ph: X_test})"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Let's plot the log-likelihood of the training and test data as\n",
    "functions of the training epoch. The quantity `inference.loss`\n",
    "is the total log-likelihood, not the loss per data point. Below we\n",
    "plot the per-data point log-likelihood by dividing by the size of the\n",
    "train and test data respectively."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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CCCFObhK8FEIc0p7+fXRnejitbu6woNc9Wx7giV1Ps6B+Hh9f+CEgePx6Z2I3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\nktQ+Nk0D21J1CQAAAADA0co95fq/ZY+rvJ6H4rZ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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11444df50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(nrows=1, ncols=1, figsize=(16, 3.5))\n",
    "plt.plot(np.arange(n_epoch), -test_loss / len(X_test), label='Test')\n",
    "plt.plot(np.arange(n_epoch), -train_loss / len(X_train), label='Train')\n",
    "plt.legend(fontsize=20)\n",
    "plt.xlabel('Epoch', fontsize=15)\n",
    "plt.ylabel('Log-likelihood', fontsize=15)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We see that it converges after roughly 400 iterations."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Criticism\n",
    "\n",
    "Let's look at how individual examples perform. Note that as this is an\n",
    "inverse problem we can't get the answer correct, but we can hope that\n",
    "the truth lies in area where the model has high probability.\n",
    "\n",
    "In this plot the truth is the vertical grey line while the blue line\n",
    "is the prediction of the mixture density network. As you can see, we\n",
    "didn't do too bad."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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AuKpTPcozFwwMMBIRDQJJr9ZmsxnBwcFdtok/22y2Ho+ZOHEi3nnnHRw6dAi5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+js7MTOnTtRU1OD2267bdxyp0+fxo4dO/D1r38dH//4x/Hmm2/iy1/+Ml544QWsWLECvb29GBkZ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\n7c3Mi9vXLsDhI52IJ5L4zbvn8cDd1+R7k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alJLQM65/wUb1GxMWcw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      "text/plain": [
       "<matplotlib.figure.Figure at 0x110f2ae10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "obj = [0, 4, 6]\n",
    "fig, axes = plt.subplots(nrows=3, ncols=1, figsize=(16, 6))\n",
    "\n",
    "plot_normal_mix(pred_weights[obj][0], pred_means[obj][0],\n",
    "                pred_std[obj][0], axes[0], comp=False)\n",
    "axes[0].axvline(x=y_test[obj][0], color='black', alpha=0.5)\n",
    "\n",
    "plot_normal_mix(pred_weights[obj][2], pred_means[obj][2],\n",
    "                pred_std[obj][2], axes[1], comp=False)\n",
    "axes[1].axvline(x=y_test[obj][2], color='black', alpha=0.5)\n",
    "\n",
    "plot_normal_mix(pred_weights[obj][1], pred_means[obj][1],\n",
    "                pred_std[obj][1], axes[2], comp=False)\n",
    "axes[2].axvline(x=y_test[obj][1], color='black', alpha=0.5)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can check the ensemble by drawing samples of the prediction and\n",
    "plotting the density of those. The MDN has learned what we'd like it\n",
    "to learn."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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vHvlfSJKEY2bOxH33349HH3kED//61xg3bhx+9ZvfYN5x4acqx7wLS4rz3xlQ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\n0el1QWSxdz48OBRYs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      "text/plain": [
       "<matplotlib.figure.Figure at 0x1110b8190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a = sample_from_mixture(X_test, pred_weights, pred_means,\n",
    "                        pred_std, amount=len(X_test))\n",
    "sns.jointplot(a[:, 0], a[:, 1], kind=\"hex\", color=\"#4CB391\",\n",
    "              ylim=(-10, 10), xlim=(-14, 14))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Acknowledgments\n",
    "\n",
    "We thank Christopher Bonnett for writing the initial version\n",
    "of this tutorial. More generally, we thank Chris for pushing forward\n",
    "momentum to have Edward tutorials be accessible and easy-to-learn."
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.12"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}
